proton spin asymmetries and d from sane-hms data · proton spin asymmetries and d 2 ... hms has...

Proton spin asymmetries and d2

from SANE-HMS data

Hoyoung Kang For SANE Collaboration

Seoul National University

APFB 2014 April 7th, 2014

Outline

• Introduction to SANE

• Experimental Setup and SANE-HMS

• Analysis: Dilution Factor and Radiative Correction

• Result: HMS Asymmetries, Structure Functions and 𝑑2 Matrix Element

• Summary

SANE - Spin Asymmetries on the Nucleon Experiment

Spin Asymmetries on the Nucleon Experiment, or SANE(TJNAF E07-003), is a measurement of the proton spin asymmetries

done in the Hall C of Thomas Jefferson National Accelerator Facility(Jefferson Lab), Virginia USA

during January-March 2009, excluding installation and commissioning periods.

Spin Structure Functions Inclusive DIS cross section depends on four structure functions, two unpolarized (F1, F2) and two polarized (g1, g2). The spin structure functions g1 and g2 can be experimentally determined by measuring spin asymmetries:

Spin structure functions When the spins of electron and nucleon are all polarized, we can see the dependence of scattering cross section on the spin structure functions 𝑔1(𝑥, 𝑄

2) and 𝑔2(𝑥, 𝑄2).

𝑔1 = 1

2 𝑒𝑖

2[𝑞𝑖+ − 𝑞𝑖

−]

𝑖

𝑔2 = 𝑔2𝑊𝑊 + 𝑔2

𝑔2𝑊𝑊 𝑥, 𝑄2 = −𝑔1 𝑥, 𝑄

2 + 𝑔1 𝑥

′, 𝑄2

𝑥′

1

𝑥

𝑑𝑥′

SANE’s purpose is to learn everything possible about Proton Spin Asymmetries and Spin Structure Functions from Inclusive Polarized DIS:

• Resonances and Q2 dependence of A2

• SSF 𝑔2 𝑥, 𝑄2

• Twist-3 effects (higher twist represents increasing interactions among partons)

• Comparing with lattice QCD, QCD sum rules

• Exploring high Bjorken x region

Purpose of SANE

World Data and SANE Region

World data lacks big region, especially in the perpendicular asymmetry. SANE-BETA covers broad region of 0.3 ≤ 𝑥 ≤ 0.8, 2.5𝐺𝑒𝑉2 ≤ 𝑄2 ≤ 6.5𝐺𝑒𝑉2

SANE-HMS covers lower 𝑄2 region.

SANE-HMS

Jefferson Lab CEBAF

Polarized electrons can be accelerated up to 6 𝐺𝑒𝑉 and the electron beam is continuous

Two linear accererators and arcs

30 Hz electron helicity flip

by peudo-random basis

SANE used 4.7 and 5.9 GeV

beam of 90 nA

Experimental Setup

ΘB = 180°

ΘB = 80°

High Momentum Spectrometer: Focused on small kinematic region

Low background Data at lower Q2 to extend RSS results

Big Electron Telescope Array: Broad kinematic region Data at intermediate Q2

High Momentum Spectrometer

HMS has smaller angular acceptance than BETA, but with precise measurement. HMS collected complementary data in SANE by varying central angle and momentum.

Resonance Spin Structure(RSS) experiment(2002) have produced meaningful results with limited HMS kinematics and data. (1.085 GeV< W <1.910 GeV and <Q2> =1.3 GeV2) Phys. Rev. Lett. 105, 101601 (2010) Phys. Rev. Lett. 98, 132003 (2007) Phys. Rev. C 74, 035201 (2006)

HMS Coverage for SANE

RSS

Q2 dependency

Extension of xBj range

Dilution Factor from Packing Fraction

The target and beam are not completely polarized. It

contains also un-polarizable materials.

𝐴 =1

𝑃𝑏𝑃𝑡𝑓

𝑑𝜎↓↑ − 𝑑𝜎↑↑

𝑑𝜎↓↑ + 𝑑𝜎↑↑

Dilution factor f is the ratio of free polarizable nucleons to the total amount of nucleons in the sample.

𝑓 =𝑁1𝜎1

𝑁1𝜎1 + 𝑁14𝜎14 + 𝑁𝐴𝜎𝐴

where 𝑁𝐴 =𝑁0𝜚𝐴𝑧𝐴

𝑀𝐴

Beam Polarization ~80%

Proton(target) Polarization ~70% Dilution Factor

Packing fraction is the relative volume ratio of ammonia to the target cell, or the fraction of the cell’s length that would be filled with ammonia by cylindrical symmetry.

Effectively


Material PF(%) Error(%p)

#2 JW 12/05 14NH3 61.0 4.32

14NH3 #13 60.7 4.22

#5 6-28-07 14NH3 59.6 4.47

#7 6-29-07 14NH3 59.6 4.47

#8 & 5 6-2x-07 14NH3 59.0 4.95

#5 & 6 6-2x-07 14NH3 56.9 4.74

#3 6/28/07 NIST irrad 14NH3 58.6 4.12

#2 6/28/07 NIST irrad 14NH3 58.8 4.34

#9 6-28-07 14NH3 61.9 4.59

#10 6-29-07 14NH3 59.4 4.44

Packing fraction

Dilution factor is calculated using MC, comparing cross sections of each materials in target cell. And packing fraction is the only necessary input for each target cell.

Dilution factor of resonance region (PF 60.9%) Dilution factor of DIS region (PF 57.2%)

Dilution factor

Radiative Correction

Following S. Stein et al., Phys. Rev. D 12, 1884 (1975),

correction was mainly done by POLRAD 2.0

Initial fit parameters came from RSS,

basically Breit-Wigner resonance

and polynomial (with some correction)

deep inelastic tail.

Newly corrected data was

refitted to iterate.

HMS Asymmetries

(1)

(3)

(2)

HMS Asymmetries

Setting Beam energy (GeV)

HMS central

momentum (GeV)

HMS angle from

beamline (degree)

< 𝑸𝟐 > 𝑮𝒆𝑽𝟐

< 𝑾 > 𝑮𝒆𝑽

(1) 4.7 (par) / 5.9 (per)

3.2 (par) / 4.4 (per)

20.2 (par) / 15.4 (per)

1.863 1.353

(2) 5.9 3.1 15.4 1.313 2.196

(3) 4.7 2.2 16 0.806 2.196

Asymmetries with(out) radiative correction

𝑄2 = 1.86 𝐺𝑒𝑉2

Asymmetries 𝑨𝟏 and 𝑨𝟐

𝐴1 and 𝐴2 are virtual photoabsorption asymmetries.

𝐴1 =𝜎1/2𝑇 − 𝜎3/2

𝑇

𝜎1/2𝑇 + 𝜎3/2

𝑇 =𝜎𝑇𝑇𝜎𝑇=𝑔1 − 𝛾

2𝑔2𝐹1

𝐴2 =2𝜎𝐿𝑇

𝜎1/2𝑇 + 𝜎3/2

𝑇 =𝜎𝐿𝑇𝜎𝑇=𝛾(𝑔1 + 𝑔2)

𝐹1

𝜎1/2𝑇 and 𝜎3/2

𝑇 are the virtual photon absorption transverse

cross sections when total helicity of photon and nucleon is 1/2 and 3/2 respectively. 𝜎𝐿𝑇 is the interference term between the transverse and longitudinal photon-nucleon amplitude.

Asymmetry 𝑨𝟏 =𝝈𝑻𝑻

𝝈𝑻

𝑄2 = 1.86 𝐺𝑒𝑉2

Asymmetry 𝑨𝟐 =𝝈𝑳𝑻

𝝈𝑻

𝑄2 = 1.86 𝐺𝑒𝑉2

Structure Function 𝒈𝟏 𝑄2 = 1.86 𝐺𝑒𝑉2

Structure Function 𝒈𝟐 𝑄2 = 1.86 𝐺𝑒𝑉2

Twist-3 matrix element 𝒅𝟐

If we ignore higher twist effects, 𝑔2is determined by 𝑔1, using Wandzura-Wilczek relation:

𝑔2𝑊𝑊 𝑥, 𝑄2 = -𝑔1 𝑥, 𝑄

2 + 𝑔1 𝑦, 𝑄2 𝑑𝑦

𝑦

1

𝑥

OPE relates the twist-3 matrix element 𝑑2 to the following:

𝑑2 = 3 𝑥2(𝑔2 −

1

0

𝑔2𝑊𝑊)𝑑𝑥 = 𝑥2 2𝑔1 + 3𝑔2 𝑑𝑥

1

0


𝑥2 2𝑔1 + 3𝑔2 , 𝑄2 = 1.9 𝐺𝑒𝑉2

𝑥


Very preliminary result of the limited 𝑥 range is

𝑑2 = −0.0072 ± 0.0004

𝑑2 = 𝑥2 2𝑔1 + 3𝑔2 𝑑𝑥

0.8

0.5

𝐴1, 𝐴2 fit evaluated at 𝑄2 = 1.9 𝐺𝑒𝑉2

SANE collaboration

U. Basel, Florida International U., Hampton U., Norfolk S. U., North Carolina A&T S. U., IHEP-Protvino, U. of Regina, Rensselaer Polytechnic I., Rutgers U., Seoul National U., Temple U., TJNAF, U. of Virginia, College of William & Mary, Yerevan Physics I.

Spokespersons: S. Choi (Seoul), M. Jones(Jlab), Z-E. Meziani (Temple), O. A. Rondon (U. of Virginia)

Summary

SANE-HMS data covers various kinematic regions and

it can produce meaningful results, besides BETA(main detector) data.

Preliminary spin asymmetry 𝑨𝟏and structure function 𝒈𝟏 shows good agreement with previous experiments.

But 𝑨𝟐 and 𝒈𝟐 show remarkable 𝑸𝟐 dependency.

Preliminary twist-3 matrix element 𝒅𝟐 of the limited x range is −0.0072 ± 0.0004.

World first proton transverse spin data on this kinematic region is expected to improve global fits.

Backup slides

Experimental goal

The goal is to get the proton spin structure functions g1 and g2 over broad range of

the Bjorken scaling variable

0.3 ≤ 𝑥 ≤ 0.8

and 4-momentum transfer

2.5𝐺𝑒𝑉2 ≤ 𝑄2 ≤ 6.5𝐺𝑒𝑉2

ep deep inelastic scattering

High-energy electron-nucleon scattering(Deep Inelastic Scattering) ep → e’X

k and k’ are the four-momenta of the incoming and outgoing electrons, P is the four-moemntum of a proton with mass M, and W is the mass of the recoiling system X.

q is the four-momentum of the virtual photon(the exchanged particle). ( 𝑄2 = −𝑞2 )

World Data of g1

C. Amsler et al., Physics Letters B667, 1 (2008)

Jefferson Lab

Thomas Jefferson National Accerator Facility

Located in Newport News, Virginia, USA

Funded by the U.S. Department

of Energy's Office of Science

Having CEBAF (Continuous

Electron Beam Accelerator Facility) and three experimental halls

UVA Target

Superconducting magnet applies 5-T magnetic field.

The target and the magnet are cooled down by liquid helium.

~140 Ghz microwave frequency causes dynamic nuclear polarization up to 90%.

Big Electron Telescope Array - BETA

BigCal

Tracker

Cherenkov

Lucite Hodoscope

Target insert

Dynamic Nuclear Polarization

The DNP process for polarizing protons, deuterons, or

any nucleus possessing a magnetic moment, requires temperatures of ;1 K or less and large magnetic holding fields. For thermal equilibrium at 1 K and 5 T, the proton polarization is only about 0.5%. However, the polarization of the “free” electrons, associated with the

paramagnetic radicals introduced into the target material, is greater than 99%. The electron polarization can be transferred to the proton through a hyperfine transition by irradiating the target with microwaves at appropriate

frequencies.

K. Abe et al., Physical Review D 58, 11203 (1998)

Dynamic Nuclear Polarization

Total yield has linear relation with packing fraction: 𝑌𝑇 = 𝑚 𝑝𝑓 + 𝑏

Using MC (P. E. Bosted and M. E. Christy, Phys. Rev., C 77, 065206 (2008))

assuming two different pf, the slope(m) and intercept(b) can be calculated and then the yield of real data produces pf of real target.

SANE packing fractions are 56% - 62% with ~4.5% error.


Comparing data with Monte Carlo results assuming 50% and 60% packing fraction of target, 60.9% packing fraction is determined for the target material #9 6-28-07 14NH3.

Data to MC ratio (W spectrum)

Packing Fraction

Packing Fraction

Data and MC comparison (Red is MC)

Fitting Function

𝐴 =1

𝑓𝐶𝑁𝑃𝑏𝑃𝑡𝑓𝑅𝐶

𝑑𝜎↓↑ − 𝑑𝜎↑↑

𝑑𝜎↓↑ + 𝑑𝜎↑↑+ 𝐴𝑅𝐶



1. Incoming and outgoing electron lose energy before and after scattering.

2. Elastic tail should be subtracted.

3. QED processes other than Born contributes to data.

ep deep inelastic scattering

C. Amsler et al., Physics Letters B667, 1 (2008)

Structure Function 𝒈𝟏 𝑄2 = 1.86 𝐺𝑒𝑉2

Structure Function 𝒈𝟐 𝑄2 = 1.86 𝐺𝑒𝑉2

Regenerated RSS result

Continuity with RSS and CLAS

Continuity with RSS

Continuity with RSS

3

Green triangles : CLAS EG1b result with Q2 = 1.2 GeV2

Red squares : RSS result with Q2 = 1.3 GeV2

Blue line : This work with Q2 = 1.313 GeV2


𝝈𝑻

Green triangles : CLAS EG1b result with Q2 = 0.844 GeV2

Red squares : RSS result with Q2 = 1.3 GeV2

Blue line : This work with Q2 = 0.806 GeV2


𝝈𝑻

Preliminary Asymmetries (2)

Very Preliminary

𝑄2 = 1.313 𝐺𝑒𝑉2

Preliminary Asymmetries (3)

Very Preliminary

𝑄2 = 0.806 𝐺𝑒𝑉2

SANE-HMS and SANE-BETA

BETA analyzed by J. Maxwell (UVA)

Systematic Errors

Error Source Average

Target Polarization 4.0%

Beam polarization 1.5%

Dilution Factor 3.0%

Radiative Corrections 10.4%

Kinematic Reconstruction 0.4%

Preliminary g1 and g2 from BETA

J. Maxwell (UVA)


𝑑2 𝑥 ≥ 𝑥𝑚𝑖𝑛 , 𝑄2 = 1.9 𝐺𝑒𝑉2

𝑥𝑚𝑖𝑛


3𝑥2(𝑔2 − 𝑔2𝑊𝑊)

𝑥2 2𝑔1 + 3𝑔2 , 𝑄2 = 1.9 𝐺𝑒𝑉2

𝑥

RSS Experiment Results

Phys. Rev. Lett. 98, 132003 (2007)

Nitrogen Correction

Borrwed Slides

Borrowed Slides

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